Abstract
The branching index (also known as the connectivity index), introduced in Milan Randic's seminal paper (J Am Chem Soc 97(23):6609-6615, 1975), is one of the the most famous, investigated, and applied among the graph-theoretical molecular descriptors. The atom-bond connectivity (ABC) index (Estrada et al in Indian J Chem A 37:849-855, 1998) and the sum-connectivity (SC) index (Zhou and Trinajstic in J Math Chem 46:1252-1270, 2009) belong to the class of successful variants of the connectivity index. In the present paper, by amalgamating the core idea of the SC and ABC indices, a new molecular descriptor is put forward-the atom-bond sum-connectivity (ABS) index. The graphs attaining the extreme values of the ABS index are determined over the classes of (molecular) trees and general graphs of a fixed order. A noteworthy property of the ABC index is that it increases when a non-isolated edge is inserted between any two non-adjacent vertices. It is proved that this property holds also for the ABS index.